Such an antenna is disclosed in numerous patent publications of the applicant, including U.S. Pat. Nos. 5,854,608, 5,945,963, 5,859,621, and 6,552,693. These patents disclose antennas each having one or two pairs of diametrically opposed helical antenna elements which are plated on a substantially cylindrical electrically insulative core of a material having a relative dielectric constant greater than 5, with the material of the core occupying the major part of the volume defined by the core outer surface. In each case, the antenna has a feed structure extending axially through the core. A trap in the form of a conductive sleeve encircles part of the core and connects to the feed structure at one end of the core. At the other end of the core, the antenna elements are each connected to the feed structure. Each of the antenna elements terminates on the rim of the sleeve and each follows a respective longitudinally extending path. In the antenna disclosed in the applicant's U.S. Pat. No. 6,369,776, the feed structure, which is a coaxial transmission line, is housed in an axial passage through the core. The diameter of which passage is greater than the outer diameter of the coaxial line. The outer shield conductor of the coaxial line is thereby spaced from the wall of the passage. This has the effect of reducing parasitic resonances. U.S. Pat. No. 5,963,180 discloses the combination of a quadrifilar dielectrically loaded antenna and a diplexer, the latter including an impedance matching network for matching the antenna to a 50 ohms load impedance at either output of the diplexer. U.S. patent application Ser. No. 11/060,215 shows how a cavity may be formed in a proximal end portion of the core to reduce the size and weight of a dielectrically loaded antenna. More complex structures are disclosed in U.S. patent applications Ser. Nos. 11/088,247, 11/742,587, 11/263,643, 60/831,334, 60/920,607 and 60/921,108. The disclosure of each of the above patents and patent applications is explicitly incorporated in the present specification by reference.